Tg‐Composition analysis of miscible polymer blends

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Abstract
Several authors have suggested a monotonic variation of the glass transition temperature (Tg) of miscible polymer blends as a function of composition. They usually express the results in terms of equations proposed by Couchman‐Karasz, Gordon‐Taylor, Fox, and several others. However, we have noticed that numerous systems exhibit a cusp when Tg is plotted as a function of composition (after correction for the presence of crystallinity when semi‐crystalline polymers are involved). This cusp cannot appear when the Tg's of the two homopolymers involved are separated by less than about 52 degrees., It will be shown that this observation is quite general since it has been observed with several polyester/chlorinated polymer blends, polycaprolactone/nitrocellulose blends, and polystyrene/poly(vinylmethylether) blends; It will also be shown that this behavior is predicted in the framework of the free volume theory, with equations derived by Kovacs. According to this theory, above a critical concentration ϕc (relative to the plasticizer) and below a critical temperature Tc, the high‐Tc, polymer no longer contributes to the free volume of the mixture whereas it does above Tc. This difference leads to a Tg‐composition variation which has to be expressed by two different equations, one below Tc and the other above Tc, the cusp defining the limit of applicability of each equation.